Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle

作者：Durdevich Micho^*; Bruce Sontz Stephen

来源：Symmetry Integrability and Geometry-Methods and Applications, 2013, 9: 040.

DOI：10.3842/SIGMA.2013.040

• Dunkl operators
• quantum principal bundle
• quantum connection
• quantum curvature
• Coxeter groups

A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.

• 出版日期2013